Missing Events in Event Studies: Identifying the Effects of Partially-Measured News Surprises

Transcription

1 Missing Events in Event Studies: Identifying the Effects of Partially-Measured News Surprises Refet S. Gürkaynak, Burçin Kısacıkoğlu and Jonathan H. Wright January 2, 2018 Abstract Macroeconomic news announcements are elaborate and multi-dimensional. We consider a model in which jumps in asset prices around macroeconomic news announcements and monetary policy decisions reflect both the response to observed headline surprises in headline numbers and latent factors, incorporating the details in the release. The details of the non-headline news, for which there are no expectations surveys, are unobservable to the econometrician, but nonetheless elicit a market response. We estimate the model by the Kalman filter, which essentially combines OLS- and heteroskedasticity-based event study estimators in one step, showing that those methods are better thought of as complements rather than substitutes. The inclusion of a single latent factor greatly increases the fit to the asset price movements bracketing macroeconomic and monetary policy announcements. JEL Classification: E43, E52, E58, G12, G14. Keywords: Event Study, Bond Markets, High-Frequency Data, Identification, Level Factor Department of Economics, Bilkent University, CEPR, CESIfo, and CFS. refet@bilkent.edu.tr Department of Economics, Bilkent University. bkisacikoglu@bilkent.edu Department of Economics, Johns Hopkins University, CEPR and NBER. wrightj@jhu.edu 1

2 1 Introduction It is notoriously difficult to establish the direction of causality among movements in macroeconomic variables and asset prices due to simultaneity and endogeneity. High frequency macroeconomic event studies have proved to be a fruitful strategy to address the issue. The event study literature studies the reaction of asset prices to news announcements, such as the employment report, GDP release or the FOMC policy announcements. It exploits the lumpy manner in which news is released to the public as a powerful source of identification (Faust et al., 2007; Gürkaynak and Wright, 2013; Kuttner, 2001). When one looks at the change in asset prices within short windows (daily or higher frequency) around news releases it is clear that asset price changes do not cause news and so identification is achieved. One can then interpret the results to make inference on macroeconomic fundamentals and beliefs of market participants about the structure of the economy. For example, Andersen et al. (2003) showed that the foreign exchange value of the dollar jumps up on the release of stronger-than-expected data in the US, which is a striking result in light of the work of Meese and Rogoff (1983) who had convinced the profession that exchange rates were a random walk, unrelated to any macroeconomic fundamentals, past, present, or future. Still, even in tight intraday windows of 20 minutes around the news announcements, event study regressions explain only a small to moderate fraction of asset price changes. Looking at the glass as half full, it is helpful to be able to link news about macroeconomic fundamentals to asset prices. Looking at the glass as half empty, it is a puzzle that we cannot explain more and indeed most of the asset price changes even around news announcements. This paper contributes to the theory and implementation of event studies. Our perspective is that macroeconomic news announcements are complex and multi-dimensional. The event study literature focuses on headline numbers and survey expectations for these numbers. We argue that these are only a part of the news release, and so the surprise is only partially 2

3 measured. For example, the US employment report that is generally released on the first Friday of each month includes aggregate employment in nonfarm payrolls and the civilian unemployment rate. The event-study literature focuses on the effects of surprises in these numbers. But the employment report also includes around 40 pages of other data. Alas, there are no survey expectations for most of these other elements, which may also elicit a market response to the extent that some of those numbers contain updates to market participants information sets surprises and are informative about macroeconomic fundamentals. In this paper, we nonetheless offer a way of capturing the non-headline surprises in data releases, in addition to the headline surprises for which we have survey expectations. Our approach, described in detail later, can be thought of as combining OLS estimation of the event-study regression with identification through heteroskedasticity. Our method helps explain the puzzle of why event study regressions explain a limited share of asset price changes. The basic idea of the method we develop comes from the heteroskedasticity-based identification literature that was proposed by Rigobon (2003) and applied very elegantly by Rigobon and Sack (2004, 2005, 2006). This approach measures the effect of an unobservable surprise simply by knowing that there are certain days on which the variance of that surprise is unusually large. Needs a connecting sentence. In considering the effects of news announcements, surveys of headline numbers have desirable properties as expectations proxies. They pass standard rationality tests and outperform simple benchmarks (Balduzzi et al., 2001). We provide further evidence on this, showing that survey-based expectations fare similar to market-based expectations, thus it is appropriate to treat the headline surprise as observed. But announcements contain information beyond the headline number. We measure the effects of other dimensions of the news announcement on asset prices using identification through heteroskedasticity. The identifying assumption is simple and incontrovertible: that there is more macroeconomic news around the times of announcements than at other times. 3

4 We propose a way of setting up the model that gives us explicit estimates of the nonheadline components of macroeconomic news surprises. To do so, we set up a model in state space form that explains a vector of high-frequency asset price changes in terms of both the observable headline surprise and a latent factor, and also fluctuations in asset prices that are unrelated to macroeconomic news. We estimate the model via the Kalman filter. The results show that the headline surprise combined with a single latent news factor that captures macroeconomic and monetary policy news, can explain a great majority of the increase in variance that comes around news announcements. We relate this latent news factor around macroeconomic releases, to announcements for which the financial press emphasize non-headline components of the data such as large revisions of past releases. Paragraph about relating our procedure to level Next, we relax the assumption of having a single factor for each release by estimating separate latent factors for separate releases. We show that the single factor is highly correlated with release specific factors on the day of these releases. This result shows that having a single factor parsimoniously explains the movements in asset prices around macroeconomic news and monetary policy decisions. Importantly, allowing for a factor that is ever present (at announcement and non-announcement windows) in addition to release specific factors, does not affect the importance of unobserved news factors. The plan for the remainder of this paper is as follows. In section 2, we discuss the eventstudy methodology, showing how it can be implemented via OLS and via heteroskedasticitybased identification, and reporting results using both methods. In section 3 we discuss why these methods are complements rather than substitutes and show how they can be simultaneously employed. Section 4 presents a discussion of the interpretation of the heteroskedasticityidentified latent release factors and goes back to the properties of the survey expectations, showing that standard reasons to doubt survey-based expectations are very unlikely to be problems in the data used in macroeconomic event studies. This section also provides a 4

5 demonstration of why it is correct to interpret the heteroskedasticity-based estimator as measuring something conceptually different from the OLS-based event study. Section 5 present robustness checks and extensions. Section 6 concludes. 2 Event-Study Methodology Macro-finance event studies relate releases of macroeconomic data and changes in asset prices to each other. For example, we may be interested in learning how, say, the five-year yield reacts to the non-farm payrolls release. We will denote the news, or unexpected, component of the macro series or monetary policy decisions being released, as s t. With forward-looking investors the log return of the asset, y t, depends on the change in the information set, hence on s t. This is why expectations surveys are important for macroeconomic news releases, they allow us to construct the unexpected component of the data release, which should drive changes in the asset prices. The general modeling setup is a system of an asset price return in a window around an event being related to a surprise that may be measured with error (Rigobon and Sack, 2006): 1 y t = αs t + ε t (2.1) s t = s t + η t (2.2) where s t is the true (but potentially mismeasured as s t ) surprise and ε t and η t are uncorrelated error terms. The parameter of interest is α, but it is not identified due to s t being unobservable. There are two ways of identifying α, via OLS and via heteroskedasticity-based identification. 1 Including simultaneity and endogeneity into this system is easy and does not change our results. We do not do so both because it leads to cluttery notation and more importantly because it is very hard to envision how these may be issues in high-frequency event studies of the type we are looking at. 5

6 2.1 OLS Identification in Event Studies If we think that measurement error is negligible s t = s t, the surprise is observable and equation (2.1) can simply be estimated by an OLS regression of y t on s t : y t = αs t + ε t (2.3) Equation (2.3) is a very simple implementation of eventstudy methodology that only requires basic OLS and the interpretation of the result is straightforward. The equation fit should be perfect if s t is the only source of variation in this window. This method requires data on expectations of upcoming announcements, but these are available from surveys, notably the long-running survey by Action Economics, which is the successor to Money Market Services (MMS), or alternatively from the Bloomberg Survey. Table 1 shows the results of such OLS-based event studies for non-farm payrolls, GDP, unemployment, durable goods orders, CPI, core CPI, PPI, core PPI, retail sales, retails sales excluding autos, average hourly earnings, the employment cost index, initial claims and FOMC policy announcements. The asset returns are changes in yields on the first and fourth Eurodollar futures contracts, and on two-, five-, ten- and thirty-year Treasury futures. The windows that we are using are from 5 minutes before the data release and FOMC policy announcement time to 15 minutes after them. Expectations are measured using MMS/Action Economics survey results. 2 Our sample period is from 1986 to 2017 for macroeconomic releases, which includes the period from December 2008 to December 2015 when the U.S. was stuck at the zero lower bound (ZLB) for short-term nominal interest rates 3. We could drop this period, but that would greatly reduce the sample size. Swanson and Williams (2014) carefully study the effects 2 The FOMC policy surprise is calculated using price changes in short dated federal funds futures contracts, as explained in Kuttner (2001). We consider FOMC policy surprises only over the 1990 to 2007 subsample. 3 A detailed explanation of the data sources and construction is relegated to Appendix A. 6

7 of the ZLB on the sensitivity of asset prices to news. While very short-term interest rates were clearly affected, the sensitivity of longer-term interest rates was essentially unchanged throughout the sample. Nonetheless in section 5 we show results from a sample ending in 2007 as a robustness check and report that our findings are about the same for this table and rest of the work that we carry out using the full sample. Results shown in Table 1 are in line with the literature (Balduzzi et al., 2001). A standard deviation non-farm payrolls surprise increases bond yields by 2 to 6 basis points. In terms of asset price responses, non-farm payrolls is by far the most important macroeconomic release. However, asset price responses to other macroeconomic announcements are also both economically and statistically significant. We see that yields at all maturities move in the same direction, but we also see a mild hump-shaped response of yields to macroeconomic announcements, meaning that the medium term maturities are affected by the macro releases the most. This resembles the level factor in that yields at all maturities are moved in the same direction by comparable magnitudes, despite the point estimates not being exactly the same. Below, we will call this common response along the yield curve the level response. We have verified that extracting a formal level factor from the yield curve and analyzing its variance would make no difference. For the monetary policy surprises, the first Eurodollar futures (ED1) response is larger than for other maturities. This is intuitive because monetary policy decisions affect the shorter term maturities the most. The findings reported in this table are also consistent with the literature going back to (Kuttner, 2001). Nonetheless, even with the very high frequency data that we have, the headline surprises explain less than 40% of the variance of the yields around news announcements. This means that there are other factors that affect the yields in this window and/or that there is measurement error in the surprises. These are often thought of as the main limitations of the OLS method. 7

8 Heteroskedasticity-based identification takes these concerns seriously and suggests an alternative way of identifying α that is robust to the existence of background noise and that does not require direct measurement of the news. 2.2 Heteroskedasticity-Based Identification in Event Studies The system of equations (2.1)-(2.2) contains four parameters, α, σ 2 η, σ 2 ε and σ 2, where σ 2 η, σ 2 ε and σ 2 are the variances of η t, ε t and s t. The variance-covariance matrix of (y t, s t ) in the event window we are looking at is: Ω E = ασ 2 α2 σ 2 + σε 2 σ 2 + ση 2 (2.4) which only has three entries, less than the number of parameters. This confirms that α is not identified without further assumptions, which we made in the OLS case by asserting that the only relevant source of variation in the event window for the measured surprise is the true surprise i.e. η = 0. Heteroskedasticity-based identification offers another way of measuring α without making those assumptions. The key insight here going back to (Rigobon, 2003) (and (Rigobon and Sack, 2004)) is that one can also look at windows where there is no event but that are otherwise comparable. Think of these windows as a period covering the same length of time, but on a day with no news announcement. We assume that in these windows the structure of (2.1)-(2.2) is the same, but there is no surprise. The variance-covariance matrix of (y t, s t ) for the non-event window is: Ω NE = σ2 ε (2.5) In the event window, we observe y t and s t, and so can estimate Ω E. Call this ˆΩ E. In the 8

9 non-event window, s t is zero by assumption, and we observe y t. We can estimate Ω NE, all elements of which are 0, except for the 1,1 element, which is informative about the variance of noise. Subtracting (2.4) from (2.5) gives Ω E Ω NE = α2 σ 2 ασ 2 σ 2 + σ 2 η (2.6) from which one can identify the parameter of interest, α. Concretely, one can simply estimate α as [ˆΩ E ] 1,1 [ˆΩ NE ] 1,1 [ˆΩ E ] 1,2, as proposed by Rigobon and Sack (2004, 2006). Table 2 shows the same exercise that was carried out in Table 1, this time using heteroskedasticitybased identification. It is striking that all coefficients are much larger when identification via heteroskedasticity is employed, compared to OLS, which could be the natural effect of correcting for attenuation bias in the measurement error model. Therefore, a possible interpretation of this finding is that headline news is indeed measured with substantial error, leading to attenuation bias, and that heteroskedasticity-based identification is robust to these problems. This is the interpretation offered by Rigobon and Sack (2006). Note that, σ η would have to be large for this. We offer a different interpretation, more in line with the evidence showing the broad efficiency of survey expectations of data releases. We argue that the survey expectations are measuring headline surprises correctly but that instead there are surprise components in news announcements that are not directly observed by the econometrician and that have important effects on asset prices. Our reasons for thinking this way, and proposed methodology to accommodate this feature of the data are presented in the next section. 9

10 3 Partially-Measured News and Heteroskedasticity-Based Identification We recognize that data releases are elaborate and multi-dimensional. The news that is captured in OLS-based event studies is only headline news, deviation of the headline number from its survey expectation. The survey expectations are well measured and usually pass standard forecast rationality tests (Balduzzi et al., 2001). Gürkaynak and Wolfers (2006) show that survey-based forecasts are comparable in efficiency to market-based ones, 4 and we expand on this argument in Section 5 below. However, it remains the case that the headline news are only a part of a news release. Releases also contain other information such as revisions to past numbers and information on sub-components. For example, the GDP release reports the contributions of different expenditure items, and markets may react differently to increases in GDP driven by gross capital formation versus inventory increases. Some releases contain a discussion of current conditions and even forecasts. The FOMC release is the obvious example, where the statement has for some time garnered more attention than the immediate policy setting. Yet in terms of news, only the headline is observable as there are surveys for these numbers alone. The balance of the news in the release is unobservable to the econometrician, but elicits a market response as well. We argue that this is why the R 2 s of OLS-based event studies are low. The regression only captures the contribution of the headline news to the variance of asset prices and effects of all other news in the same release show up in the residual. Notice that with this interpretation the OLS-based event study answers a narrowly defined question correctly: it determines the relationship between the headline news (but not the whole 4 We focus on surveys of expectations of events that will take place within a week s time. cite The literature on surveys of expectations for longer-horizon outcomes, such as expectations of inflation in a year routinely find forecasting anomalies but despite this Ang et al. (2007) show that survey expectations remain the best forecaster among many alternatives. 10

11 news release) and the asset price in question. The heteroskedasticity-based estimator instead allows the news to be unobservable and conditions only on the time of the data release. To the extent that news are multidimensional, the increase in variance at the time of the release is due to more than the headline surprise. The heteroskedasticity-based estimator captures the asset price response to the news release as a whole, not only to the headline number. This, rather than sizable measurement error in survey expectations, is why the heteroskedasticity-based estimator always finds larger asset price response coefficients. In the next section, we show this analytically, and bring direct evidence to verify that heteroskedasticity-based estimator, along with the headline surprise effects, captures the effects of non-headline component of the release. We therefore posit a holistic understanding of the yield changes in news release event windows is possible, using OLS to partial out the effects of the observable news on the asset prices, and then using heteroskedasticity-based identification to find out the effect of non-headline, unobservable news in the data release. This could be done in two steps, with heteroskedasticity-based identification applied to residuals from the OLS but we instead introduce an efficient, one-step estimator via the Kalman filter. This has the useful byproduct of giving an estimate of the unobserved news component in any given data release, which is not directly available from identification through heteroskedasticity. We let y t denote the 6x1 vector of yield changes on all days from 8:25am to 8:45am and from 2:10pm to 2:30pm. Some days have macroeconomic announcements at 8:30am, while others do not, but all the macroeconomic announcements that we consider come out at 8:30am. Similarly, some days have FOMC announcements around the latter event window (with some minor deviations of timing to accommodate FOMC announcements times early in the sample), and some do not. 11

12 The model that we specify is that y t = β s t + d t γ f t + ε t (3.1) where s t is the vector of surprise of the 13 types of macroeconomic announcements (as given in section 2) and the FOMC policy surprise 5, d t is a dummy that is 1 on an announcement window and 0 otherwise, f t is an iid N(0, 1) latent variable and ε t is iid normal with mean zero and diagonal variance-covariance matrix. Macroeconomic announcement expectations are again measured using the MMS/Action Economics survey and FOMC policy surprises are calculated following (Kuttner, 2001). The sample period is for macroeconomic releases and for FOMC policy surprises. If the f t term were dropped, equation (3.1) would collapse to the standard OLS event study regression and if the s t term were dropped it would collapse to a heteroskedasticitybased estimator. As it stands, this equation can be estimated by maximum likelihood via the Kalman filter. 6 The results are reported in Table 3, for both the macro news and monetary policy implementations. Table 3 also reports the R 2 values from the regressions of y t on s t alone, and from regressions augmented with the Kalman filtered estimate of f t in equation (3.1), on announcement days only. The headline surprise alone explains less than 40% of announcement-window variation in each of the yields considered here, as was shown in Table 1. Augmenting the regression with one latent factor brings the explained share up to 98%. Basically we can explain about all of the movements in the term structure of interest rates around news announcements with the headline surprise and one latent factor. Inclusion of the latent factor makes little difference to the estimated coefficients on the headline surprises, although it does reduce the error variance 5 s t is set to 0 for any announcement that does not take place in that window 6 The EM algorithm underlying the Kalman filter is conceptually straightforward but computationally demanding. Our code can handle any number of releases, asset price changes and latent factors and is made available for others to use. 12

13 and hence the standard errors. We discuss the largest observations of this factor in Section 4, showing that they indeed correspond to days where the market commentary emphasizes non-headline components of the data releases. The specification in equation (3.1) implies that the latent factor has the same loadings for all announcement types. However, in practice it seems likely that the latent factor would, for example, have larger variance around employment reports than around other announcements. 7 We can extend the model to incorporate these features, specifying instead that: y t = β s t + Σ I i=1d it γ i f it + ε t (3.2) where d it is a dummy that is 1 if an announcement of the ith type comes out on day t and zero otherwise and I is the number of announcements. 8 The factors {f it } I i=0 are all standard normal and are independent over time and independent of each other. This extended model can also be estimated by maximum likelihood via the Kalman filter. The results are reported in Table 4. The coefficient estimates on the headline surprises are similar to those in Tables 1 and 3. Table 4 also includes the R 2 values from the regressions of elements of y t on s t alone, and from regressions augmented with the Kalman smoothed estimates of the latent factors associated with macro announcements. Incorporating the macro factors increases the R 2 values for yield changes from below 40% once again to above 90% for most maturities. It is important to point out that the R 2 s are similar to the single factor case. This is intuitive because the single factor model is the restricted model that assigns a common factor for all the releases whereas the model with release specific factors is the unrestricted model, 7 Since variances of latent variables are normalized to unity to identify them, larger variances will manifest themselves as larger coefficients. 8 Because they always come out concurrently, non-farm payroll/unemployment/average hourly earnings, retail sales/retail sales ex autos, core PPI/PPI and core CPI/CPI surprises share a single latent factor associated with these releases and so there are 9 macroeconomic latent factors even though there are 13 macroeconomic announcements. In this model I = 9, including a factor for the FOMC release. 13

14 allowing heterogeneity among the releases. Hence mechanically, R 2 s of the latter cannot be lower than the former. We discuss this finding and relationship to the level factor of yield curve movements in section below. We repeated this exercise using daily data, with changes in Treasury yields as independent variables rather than Treasury futures rates. The results, not reported, show that for all surprises, the estimated coefficients are similar to their intraday counterpart. However, these coefficients have higher standard errors and the regressions have smaller R 2 s. This result is intuitive: There are other financial market developments happening on a given day along with macroeconomic announcements. This introduces additional noise to the event study regression. Nonetheless, when the latent factor is introduced the fraction of yield changes explained once again dramatically increase. Daily results not reported show that there is an empirical regularity that is not special to using intraday data. 4 Discussion: Understanding the latent factor In this section we study the relationship between measurement error, latent factors, OLS and heteroskedasticity-based estimators. To do so, we analytically explore the implications of different modeling assumptions about the data generating process on OLS and heteroskedasticitybased estimates and offer direct empirical evidence to rule out cases that are inconsistent with the data. We then study the properties of the latent factor and show that it is indeed related to non-headline news and further that incorporating these non-headline news effects help explain about all of the level variation in the yield curve. 4.1 A General Model Here we show that, a model with one latent factor and no measurement error in surprises and a model with measurement error in surprises but with no latent factor similarly produce 14

15 higher heteroskedasticity-based parameter estimates compared to the OLS estimates. That is, looking at the difference between heteroskedasticity-based and OLS estimates of event study coefficients, an econometrician cannot identify if identification through heteroskedasticity method is measuring non-headline components of the news or correcting for possible attenuation bias. We formally show this here and present empirical evidence that will help distinguish between the cases in the following subsection. First we consider a general model which incorporates measurement error and an unobservable latent factor. The model given in section 2 can be written as: y t = β s t + γ d t f t + ε t s t = s t + η t where y t is the vector of yield changes around event windows, s t is the observed surprise, s t is the true headline surprise, d t is a dummy that is 1 on an announcement day and 0 otherwise, f t is an iid N(0, 1) latent variable, ε t and η t are iid processes measuring noise in yields and measurement error of headline surprise. For ease of notation we will treat y t as a scalar but obviously in our method the latent f t can only be extracted from a vector y t. Here parameter β is the parameter of interest. To estimate this parameter using OLS and identification through heteroskedasticity, we need the variance-covariance matricies for event (Ω E ) and non-event (Ω NE ) windows: Ω E = β2 σs 2 + γ2 + σε 2 βσs 2. σs 2 + σ η 2 Ω NE = σ2 ε

16 In this general model, the OLS estimate for β is cov(yt,st) var(s t) which equals to: ˆβ OLS = ˆΩ E 1,2 ˆΩ E 2,2 and the identification through heteroskedasticity estimate of β is: ˆβ HET = ˆΩ E 1,1 ˆΩ E 1,2 ˆΩ NE 1,1 where Ω i,j denotes the i th row and the j th column entry of the relevant variance-covariance matrix. Now we can work out the possible biases of the two estimators when none, one, or both of latent factor or measurement error are present. This general model collapses to a model with no latent factor if γ = 0 and the no measurement error case (the case presented in this paper) is when ση 2 = 0. 9 Case ˆβOLS ˆβHET 1. γ = 0, σ 2 η = 0 β β 2. γ = 0, σ 2 η 0 β(1 σ2 η σ 2 s +σ 2 η ) β 3. γ 0, σ 2 η = 0 β β + γ2 βσ 2 s 4. γ 0, σ 2 η 0 β(1 σ2 η σ 2 s +σ 2 η ) β + γ 2 β(σ 2 s +σ 2 η ) In the case with a latent factor the heteroskedasticity-based estimator gives β + γ2. If the βσs 2 variance of the latent factor were not normalized to unity, this would be β(1 + γ2 σ 2 f ) with the β 2 σ 2 s bias being proportional to γ2 σ 2 f, which is positive and always biases the heteroskedasticitybased estimate upwards. It is instructive to note that this term captures the relative variance shares of the latent and headline factors in the event window changes of the yields. As the 9 The derivation is given in the Appendix. β 2 σ 2 s 16

17 relative variance share of the latent factor increases (non-headline news carry more information affecting yields), the bias of the heteroskedasticity-based estimator increases. If there are neither a latent factor nor measurement error in the surprise, the OLS and heteroskedasticity based estimators both uncover true β and should coincide as in case 1. However, as Tables 1 and 2 show, these are significantly different from each other, implying that this is not the relevant case. The other three cases however, require more information than OLS and heteroskedasticitybased estimates to distinguish. In case 2, the OLS estimate will be biased down due to attenuation bias but the heteroskedasticity-based estimator still covers the true β, which will always be larger than the OLS estimate in absolute value, as is the case in the data. However this observation is not enough to conclude that there is measurement error. Case 3 shows that in the absence of measurement error in headline surprise, if there is more information revealed in the release, heteroskedasticity-based estimator will be larger than the OLS estimate in absolute value. Of course, in this case the OLS will estimate the true β while the heteroskedasticity-based estimator will be biased upwards. These two maladies do not interact with each other, hence if both are present in the data, OLS will be biased down and the heteroskedasticity-based estimate will be biased upwards, as in case 4. Based on only the OLS and heteroskedasticity-based estimates of β, the three cases above are observationally equivalent. To distinguish between these alternative interpretations and support our interpretation of the presence of a latent factor we check if the following conditions are consistent with the data: 1. Measurement error in survey-based surprises are negligible. 2. For events with known larger non-headline components, the distance between the heteroskedasticitybased and OLS estimates should be greater than the distance with smaller non-headline components. 17

18 If the first condition holds in the data, then σ η 0, hence σ 2 s σ2 s, which rules out cases 2 and 4. However, for completeness, it still needs to be shown that the non-headline component of the news is the reason for the differences in the OLS and heteroskedasticity-based estimates, captured by γ2 βσ 2 s in case 3. Below we provide empirical evidence supporting these two conditions. First, we bring in data from economic derivatives to show that measurement error in the survey-based surprise is likely to be negligible for eventstudies. Next, we show that heteroskedasticity-based and the OLS estimators differ more for events with known larger non-headline news. To do so, we compare monetary policy announcements with and without accompanying statements. We show that heteroskedasticity-based estimates are closer to the OLS counterparts on days without monetary policy statement compared to the days with statements. 4.2 Efficacy of survey expectations The surveys used in event studies are those of news releases that are to take place very soon, no longer than a week after the time of the survey. And the event is the release of information on something that has already taken place, such as the industrial production reading for the previous month. Hence, these expectations are not subject to the over persistence often reported in analysis of long-term expectations (Fuhrer, 2017). However, three areas of concern remain: (i) The survey expectation may be dated, there may be incoming news between a respondent s reporting of her expectation and the releases which change her expectations, (ii) respondents may not have sufficient skin in the game, reporting an unreasonable number just to be done with the survey, (iii) especially if the survey responses are made public with the respondents names, they may have an incentive to be right in the extreme case, not on average, therefore reporting numbers closer to the tails rather than their true expectations. We show that while these concerns sound relevant, in practice survey expectations work remarkably 18

19 well and are not subject to large measurement errors. To do so, we compare the survey-based expectations and surprises based on these to those of timely market-based expectations. The data comes from (Gürkaynak and Wolfers, 2005) where they analyze the market for Economic Derivatives. This was a market, now defunct, where Deutsche Bank and Goldman Sachs allowed trades of binary options on news releases about half an hour before the release itself. These call options paid off if the release came in at or above the buyer s strike price. Gürkaynak and Wolfers describe the market and these options, as well as the methodology to use them to construct risk neutral probability density functions of market perceived data release outcomes. Their analysis is on the relationship between the market implied uncertainty and the survey implied heterogeneity of expectations. In his discussion of that paper Chris Carroll (2005) notes how remarkable it is that in terms of the first moments the survey- and market-based expectations are so similar to each other. We formalize his argument here. Market-based expectations of data releases are not subject to any of the potential measurement error problems survey-based ones may be subject to. The market operates minutes before the data release, hence there is no scope for staleness; the traders do have skin in the game as they bet on their expectations; and since the market returns are anonymous they have no incentive to get low probability events right. We construct market- and survey-based expectations and news surprises based on these and directly test whether there is measurement error in survey-based expectations by comparing the market responses to the two surprise measures. If there is indeed sizable measurement error in survey-based surprises event study coefficients based on these should be significantly smaller than coefficients based on Economic Derivatives-based surprises which are not subject to measurement error. Thus we run SUR exercises for the four releases covered by Economic Derivatives (Nonfarm payrolls, NAPM, 19

20 Retail Sales ex-autos, and Initial Claims) of the form y t = y t = 4 θi s surveysurprise it + ε t (4.1) i=1 4 θi m econderivsurprise it + ε t (4.2) i=1 Measurement error in survey expectations will lead to smaller θ s compared to θ m. Table 5 reports the results as well as the joint test that θ s i = θ m i. It is very striking that while all θ s i are somewhat smaller than corresponding θ m i (consistent with minor classical measurement error) the differences in point estimates are very small and in no cases individually or jointly statistically significant. Survey expectations capture market expectations extremely well. Even if one disregards the statistical equality of the coefficients and attributes all of the difference between point estimates to measurement error, the differences are on the order of about 5 to 15 percent, an order of magnitude smaller than the differences between OLS and heteroskedasticity-based estimates shown in tables 1 and 2. We conclude that survey-based expectations capture market expectations strikingly well and that substantial differences between OLS and heteroskedasticity-based estimates of asset price reactions to incoming macroeconomic data cannot be due to measurement error in surveys and bias in the coefficients. 4.3 Comparison of OLS and Heteroskedasticity-Based Estimates A well studied and well understood case of multi-dimensional data release is that of FOMC announcements, which contain both the interest rate decision and an accompanying statement providing information on the future course of interest rates. This is a case we will return to in more detail but here we will exploit the fact that FOMC releases did not always contain 20

21 statements. Until 1994 FOMC did not issue statements and until 1999 statements were only issued when the policy rate was changed. If OLS and heteroskedasticity-based estimates are fundamentally measuring the same quantity the difference between the two should not depend on the presence of an accompanying statement. If on the other hand, as we suggest, heteroskedasticity-based identification provides the asset price response to the whole event rather than the headline, the difference between the two measures should be larger when the non-headline event component has higher variance. 10 Increasing the variance of non-headline news is exactly what the FOMC did when it began to issue statements. So, if our conjecture is correct, the coefficient estimates of the impact of FOMC announcements on yields measured by OLS- and heteroskedasticitybased estimators should be closer for a sample of events consisting of policy actions only and farther away for a sample consisting of announcements that also have statements providing information on the policy path. For monetary policy surprises, as before, we follow the standard procedure and use Federal Funds Futures-based surprises as suggested by (Kuttner, 2001). Table 6 shows that when statements do not accompany the policy rate decision the OLS- and heteroskedasticity-based estimates of the asset price reactions are quite similar albeit the OLS estimates always being smaller due to market participants inference of information even in the absence of formal statements but for the sample that includes statements the heteroskedasticity-based estimator finds a reaction coefficient that is two to 400 times larger than the OLS coefficient. What is striking here is not that OLS coefficients are a little smaller and statistically less significant in the latter sample. This is due to the dearth of policy action surprises in the 21st century, when policy actions were usually signaled ahead of the FOMC meeting date. What is noteworthy is the increase in the spread between OLS- and heteroskedasticity- 10 This is not apparent from the algebra in section 4.1 as the variance of the latent factor is normalized to unity. But the larger the true variance of the latent factor, the larger the absolute value of γ will be. 21

22 based estimators, and the fact that the spread becomes significantly more pronounced as maturity increases. This is exactly what one would expect to find based on our conjecture: the presence of a statement will increase the distance between OLS- and heteroskedasticity-based estimates for all maturities but as the statement is more informative for longer maturities 11 the heteroskedasticity-based estimator, which combines the action and path (statement) surprises, will find even larger coefficients for those maturities. This is precisely what the data shows in Table 6. Thus, by studying the FOMC announcement dates, we conclude that the heteroskedasticitybased estimator provides a convolution of the asset price responses to the headline and non-headline components of news, whereas our partial observability-based Kalman filtering methodology provides asset price responses to headline news and the latent non-headline news component separately. An additional benefit is that this method estimates the latent component so that its properties can be studied and subjected to statistical testing, which we now turn to. 4.4 Latent factor and heteroskedasticity-based estimates In this subsection we show the relationship between the latent factor and heteroskedasticitybased estimates. Specifically, we show that the heteroskedasticity-based estimate is mechanically the sum of the effects of headline and non-headline news on asset prices. However, this exercise requires identifying γ 2. Below we propose a to apply this method to the eventstudy residuals. If our interpretation is correct, once the variation due to observable factors is taken out from the variation in asset prices around a tight even window, what is left should be the variation caused by the unobserved component of news releases. Given that survey-based surprises have negligible measurement error, true headline sur- 11 The literature, described in the next section, finds quantifying the statement helps explain the movement in longer maturities, whereas short maturities are more responsive to the immediate policy action. 22

23 prises are equal to observed surprises. Hence the general model becomes: y t = βs t + γd t f t + ε t In a usual eventstudy setup, β can be separately identified by OLS and on an event day the residual of this regression is: φ t E = γ f t + ε t On a non-event day: φ t NE = ε t We have the following event and non-event variance-covariance matricies for φ t : Ω φ E = γ2 + σε 2 0. σs 2 Ω φ NE = σ2 ε Heteroskedasticity-based estimator for γ 2 is given by ˆΩ E NE 1,1 ˆΩ 1,1. Even though this method identifies γ up to a sign, the object of interest is γ 2 which helps identify γ2. βσs 2 Table 7 shows the heteroskedasticity-based estimates as given in Table 2, the OLS estimates ˆβ and ˆγ2 ˆβˆσ 2 s for macroeconomic and monetary policy news and their sum. 12 sum is equal to the heteroskedasticity-based estimator. 13 The We have thus decomposed the heteroskedasticity-based estimate into its components due to observable and unobservable factors and also shown that our procedure is a one-step efficient implementation of sequential OLS and heteroskedasticity-based estimator applications. This is an indication that the extra 12 The OLS estimates for the announcements differ from Table 1 because days with multiple releases are drop as we did for the identification-through-heteroskedasticity estimation. 13 They are not always identical due to small sample, which we verify using a Monte Carlo experiment. The results can be found in the Appendix. 23

24 term in the heteroskedasticity-based estimator is not the bias, but the extra effect coming from the release of the statement. To further strengthen this point, in the next subsection, we relate the latent factor to monetary policy statements and macroeconomic releases. 4.5 Interpreting the Latent Factor So far we have focused on the relationship between the heteroskedasticity-based, OLS and Kalman filter based estimators and showed that a single factor estimated using the Kalman filter along with observable headline surprises is sufficient to explain the variation in asset prices around macroeconomic news events. In this subsection, we closely examine the economic interpretation of the latent factor. Figure 2 shows the time series of the latent factor estimated by our Kalman filter around FOMC announcement windows. As expected the factor is small and dormant in the period before FOMC began to issue statements, and much larger and volatile when statements began to accompany policy decisions, consistent with the findings in subsection 4.4. Table 8 lists the five largest readings of the latent factor on FOMC announcement windows and shows that based on the comments in the financial press, these are indeed days of well-known statement surprises. Monetary policy statement surprises are well understood and it is reassuring that the latent factor we extract behaves as expected. Non-headline surprises in other macroeconomic data releases are much less well understood. Nonetheless, similar to FOMC announcement windows, we look at the largest readings of the latent factor and turn to financial press to see whether non-headline components were emphasized on the days the non-headline news factor spiked. Looking at the ten largest readings of the latent macro factor, in Table 9, we see that these too correspond to days where the financial press emphasized non-headline news. In 24

25 particular, the first entry, with the largest latent factor, is an employment report containing a very sizable upwards revision of past two months payroll numbers. Again, this is exactly what the latent factor was designed to capture. Looking at the other entries in the list, we see that all the other entries are either related to other revisions or subcategories of the releases such as inventory figures, average length of unemployment or wages which are not headline news but are part of the statement itself. As expected, the latent variable spikes most often on employment report dates, with four of the five largest readings coming from this release Why is a Single Factor Sufficient? One of the most interesting findings of this paper is that a single latent factor is sufficient to capture almost all of the (non-headline) variation in yields around news releases. This would have been surprising if a single factor per release were sufficient revisions and private vs public payrolls changes being captured by the same latent factor for the employment report but it is very surprising as a single factor across releases is sufficient. While initially counterintuitive, this finding ties naturally to the dominance of the level factor in yield curve movements. As noted before in Table 1, observed macroeconomic news surprises have a level effect on the yield curve. 14 The latent factor for each release also elicit a level effect, as does common latent factor. In this paper we remain silent on why the yield curve responds with a level shift to incoming macroeconomic news. 15 It is however, very important to have shown that level reaction can be tied to macroeconomic news releases. Imposing a common factor across releases imposes a restriction. The fact that fit of the 14 The coefficients suggest a mild hump but we call the response level nonetheless. Forcing their coefficients to be exactly level would not have changed our results, hence we call this level-like effect without distorting the analysis. 15 One author of this paper has work arguing that the level effect is due to updating of steady state inflation beliefs ((Gürkaynak et al., 2005b)), another has argued that it is due to changes in expected real rates ((Beechey and Wright, 2009)) and the third has argued that neither explains the yield curve behavior in a model consistent way (Kısacıkoğlu, 2016). We do not get into that question in this paper. 25

26 regression (the Kalman filter fit) does not deteriorate compared to release specific factors imply that the restriction is correct. Indeed, since all factors have the same level shape, combining them into a single, level factor does not compromise the fit. Individual latent factors are different scalings of the common factor. In Figure 1 we show the correlation of the common factor with the individual latent factors and show that there is almost perfect correlation. A corollary of this argument is that all news, observed or unobserved, have the same effect on the yield curve, hence we could have treated the headline news as unobservable as well and only extracted a single latent factor, without compromising the fit. Table XX shows, the result of this exercise. Indeed the fit is about the same. Note that mechanically these are the heteroskedasticity-based estimator effects but our methodology allows measuring R 2, and showing that the fit remains about the same when all news are treated as unobservable. It is important to emphasize the two separate findings here. The first is that observed and latent news both elicit level responses from the yield curve, as shown by the regression coefficients. The second is that the level factor in the event window is almost completely explained by those observed and latent factors, as shown by the R 2 s. We therefore finally have an understanding of what drives level. A natural question to ask is whether this finding may be due to a noise-like ever present level factor and not specific to the event window. In the next section we show that this is not the case. In the event window news drive the level factor. 5 Extensions and robustness There are several extensions and robustness checks that are in order. An obvious robustness check is to limit the sample to the period before the financial crisis, so that estimates will not be affected by the short end being stuck at zero. Another one is to verify that the latent factor, which is essentially a level factor, is not just capturing a level factor that is always in 26